Reduce to lowest terms: $- \dfrac{1}{8} \div - \dfrac{3}{4} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{3}{4}$ is $- \dfrac{4}{3}$ Therefore: $ - \dfrac{1}{8} \div - \dfrac{3}{4} = - \dfrac{1}{8} \times - \dfrac{4}{3} $ $ \phantom{- \dfrac{1}{8} \times - \dfrac{4}{3}} = \dfrac{-1 \times -4}{8 \times 3} $ $ \phantom{- \dfrac{1}{8} \times - \dfrac{4}{3}} = \dfrac{4}{24} $ The numerator and denominator have a common divisor of $4$, so we can simplify: $ \dfrac{4}{24} = \dfrac{4 \div 4}{24 \div 4} = \dfrac{1}{6} $